# Thread: Solving Logarithmic equation

1. ## Solving Logarithmic equation

I'm wondering if anyone can help, I'm stuck with the following logarithmic equation:

x^3*ln(x)-4x*ln(x)=0

I can easily see why x=1 is a solution (ln(1)=0).Is this the correct procedure for finding the other solutions:

=(x^3-4x)*ln(x)

=x(x^2-4)*ln(x)

=x((x+2)(x-2))*ln(x)

x= -2 or +2

The mark scheme for the past paper says the 2 answers are 1 and -2, but I can't see why 2 isn't a valid solution also? Also, is x=0 not a solution because ln(0) is not defined?

2. ## Re: Solving Logarithmic equation

Originally Posted by simon238
I'm wondering if anyone can help, I'm stuck with the following logarithmic equation:

x^3*ln(x)-4x*ln(x)=0

I can easily see why x=1 is a solution (ln(1)=0).Is this the correct procedure for finding the other solutions:

=(x^3-4x)*ln(x)

=x(x^2-4)*ln(x)

=x((x+2)(x-2))*ln(x)

x= -2 or +2

The mark scheme for the past paper says the 2 answers are 1 and -2, but I can't see why 2 isn't a valid solution also? Also, is x=0 not a solution because ln(0) is not defined?
I think your mark scheme is off because the valid solutions for this are x=1 and x=2.

You are correct about 0 not being valid because log(0) is not defined and assuming you are solving over the real numbers the same goes for x=-2.

3. ## Re: Solving Logarithmic equation

Ahh yes, of course, thank you. I guess I just took the mark scheme as gospel, but I couldn't make sense of it